A change of variable formula with applications to multi-dimensional optimal stopping problems

Cheng Cai and Tiziano De Angelis

Papers from arXiv.org

Abstract: We derive a change of variable formula for $C^1$ functions $U:\R_+\times\R^m\to\R$ whose second order spatial derivatives may explode and not be integrable in the neighbourhood of a surface $b:\R_+\times\R^{m-1}\to \R$ that splits the state space into two sets $\cC$ and $\cD$. The formula is tailored for applications in problems of optimal stopping where it is generally very hard to control the second order derivatives of the value function near the optimal stopping boundary. Differently to other existing papers on similar topics we only require that the surface $b$ be monotonic in each variable and we formally obtain the same expression as the classical It\^o's formula.

Date: 2021-04, Revised 2023-07
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Citations: View citations in EconPapers (3)

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